In a damning verdict, committee chair Meg Hillier said the “unacceptable and entirely avoidable situation stems from multiple failures on the part of the Department”.

Her committee found that the DWP expects to pay out £340 million in arrears by April next year but claimants could still be left as much as £150 million short because the department does not plan to make up for underpayments dating from before October 2014.

And those affected will not be reimbursed for benefits such as NHS prescriptions, dentist’s treatment and free school meals which they missed out on because of the DWP’s mistake.

Of the people affected, more than 20,000 of those most in need are owed around £11,500 each and some as much as £20,000

Ms Hillier described the DWP’s response to the problem with ESA payments as “blinkered and wholly inept”, and said it revealed “weaknesses at the highest levels of management”.

The committee gave the department until October this year to report back on action it is taking to ensure mistakes are not repeated. And it said the DWP should provide a figure for the total amount claimants have missed out on, along with an explanation of how it will provide “appropriate remedies”.

The committee said: “There is clearly much more to be done to right this wrong. We encourage the department to act swiftly, decisively and comprehensively to address the harm caused by this mistake and, more broadly, to give much greater priority to correcting benefit underpayments to vulnerable people.”

Those affected were people whose ability to work is affected by disability or illness, who were transferred from the old incapacity benefit on to ESA from 2011 onwards. Some 70,000 ended up being underpaid for years, losing an average of £5,000, found the report. Of these, more than 20,000 of those most in need are owed around £11,500 each and some as much as £20,000.

The committee gave the department until October this year to report back on action it is taking to ensure mistakes are not repeated

The report found that the “unacceptable and entirely avoidable” situation came about because of “multiple failures” by the DWP. The department failed to listen to staff, claimants or experts when they warned that things were going wrong and failed to scrutinise its own processes properly or to ensure that they reflected the legislation, said the committee.

And a “culture of indifference” at the department meant it took more than six years to take action, even though it was “painfully obvious” that a significant number of claimants were being underpaid.

“Thousands of people have not received money essential for living costs because of Government’s blinkered and wholly inept handling of ESA,” said Ms Hillier.

“The department simply didn’t listen to what claimants, experts, support organisations and its own staff were saying. Its sluggishness in correcting underpayments, years after it accepted responsibility for the error, points to weaknesses at the highest levels of management. Indifference has no place in the delivery of vital public services. It must be rooted out wherever it is found.

The report has found that the department failed to listen to staff, claimants or experts when they warned that things were going wrong

“The department needs to explain what it is doing to improve both its management culture and its ability to gather and act promptly on critical intelligence.

“It must also set out how it will more quickly address the £1.7 billion of underpayments claimants miss out on each year.”

A DWP spokesman said: “We take the issue of underpayments very seriously and have actively taken steps to put this right as quickly as possible, to ensure people get the support they are entitled to. We have recruited 400 extra staff and have already started making payments - over £40 million so far. We have continued to provide regular updates to both the PAC and the House in regards to the progress of these repayments, and will continue in this stead.”

In a separate development, the chairman of the Commons Work and Pensions Committee wrote to employment minister Alok Sharma to raise concerns over benefit sanctions data supplied by the DWP.

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Frank Field said that the department’s published data “consistently understate” the sanctions applied to claimants by removing those who have successfully appealed against decisions.

And he queried the decision to sanction 1,108 Universal Credit claimants in February alone despite them being judged medically unfit to work or look for work.

“What is the point of applying sanctions to people who cannot work and are not expected to look for jobs?” asked Mr Field. Benefit sanctions are the only major welfare reform this decade to have never been evaluated, and the picture DWP paints of the policy doesn’t match the troubling stories we’ve heard.”